Related papers: Finite Logarithmic Order Meromorphic Solutions of …
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
In this paper, we have found that some certain Fermat-type shift and difference equations have the meromorphic solutions generated by Riccati type functions. Also we have solved the open problems posed by Liu and Yang (A note on meromorphic…
The Lemma on the Logarithmic Derivative of a meromorphic function has many applications in the study of meromorphic functions and ordinary differential equations. In this paper, a difference analogue of the Logarithmic Derivative Lemma is…
In this paper, we continue to study the sharing value problems for higher order derivatives of meromorphic functions with its linear difference and $q$-difference operators. Some of our results generalize and improve the results of…
This article contains the theorems which shows that when $A(z)=h_1(z)e^{P_1(z)}$ and $B(z)=h_0(z)e^{P_0(z)}$ are of same order,then all the non-trivial solutions of equation $f"+A(z)f'+B(z)f=0$ are of infinite order. Moreover we extend…
In this paper, we study the growth of transcendental entire solutions of linear difference equations \begin{equation} P_m(z)\Delta^mf(z)+\cdots+P_1(z)\Delta f(z)+P_0(z)f(z)=0,\tag{+} \end{equation} where $P_j(z)$ are polynomials for…
In this paper, we investigate the delay differential equations of Malmquist type of form \begin{equation*} w(z+1)-w(z-1)+a(z)\frac{w'(z)}{w(z)}=R(z, w(z)),~~~~~~~~~~~~~~(*) \end{equation*} where $R(z, w(z))$ is an irreducible rational…
For differential equations $P(y^{(k)},y)=0,$ where $P$ is a polynomial, we prove that all meromorphic solutions having at least one pole are elliptic functions, possibly degenerate.
Recent work of C. Fefferman and the first author has demonstrated that the linear system of equations \begin{equation*} \sum_{j=1}^M A_{ij}(x)F_j(x)=f_i(x)\hspace{.2in} (i=1,...,N), \end{equation*} has a $C^m$ solution $F=(F_1,...,F_M)$ if…
In this paper, we will prove that all non-trivial solutions of $f''+A(z)f'+B(z)f=0$ are of infinite order, where we have some restrictions on entire functions $A(z)$ and $B(z)$.
The meromorphic solutions $f$ with $\rho_2(f)<1$ of the non-linear difference equation \begin{align*} f^n(z)+P_d(z,f)=p_1e^{{\lambda_1}z}+p_2e^{{\lambda_2}z}+p_3e^{{\lambda_3}z}, \end{align*} are characterized in terms of exponential…
In this paper, we describe the automorphic properties of the Fourier coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier coefficients of…
Given an entire function $f$ of finite order $\rho$, let $L(z,f)=\sum_{j=0}^{m}b_{j}(z)f^{(k_{j})}(z+c_{j})$ be a linear delay-differential polynomial of $f$ with small coefficients in the sense of $O(r^{\lambda+\varepsilon})+S(r,f)$,…
Let $\mathbb{F}_q$ be the finite field of $q$ elements and $a_1,a_2, \ldots, a_k, b\in \mathbb{F}_q$. We investigate $N_{\mathbb{F}_q}(a_1, a_2, \ldots,a_k;b)$, the number of ordered solutions $(x_1, x_2, \ldots,x_k)\in\mathbb{F}_q^k$ of…
We consider properties of binomial series $\sum_{n=0}^\infty a_n z^{\underline{n}}$, where $z^{\underline{n}}=z(z-1)\cdots(z-n+1)$ and the convergence of binomial series in the complex domain. The order of growth of entire and meromorphic…
In this paper, we will give estimates for the logarithmic derivative $ \left\vert \frac{f^{\left( k\right) }\left( z\right) }{f\left( z\right) } \right\vert $ where $f$ is a meromorphic function in a region of the form $ D\left( 0,R\right)…
We introduce a general third order non-linear autonomous ODE which covers many ODEs coming from boundary layer problems, like the Falkner-Skan equation and the Cheng-Minkowycz equation. Using Wiman-Valiron theory and complex analytic…
In the work, we focus on a conjecture due to Z.X. Chen and H.X. Yi[1] which is concerning the uniqueness problem of meromorphic functions share three distinct values with their difference operators. We prove that the conjecture is right for…
Based on the analysis of a certain class of linear operators on a Banach space, we provide a closed form expression for the solutions of certain linear partial differential equations with non-autonomous input, time delays and stochastic…
After introducing q-analogues of the Borel and Laplace transformations, we prove that to every formal power series solution of a linear q-difference equation with rational coefficients, we may apply several q-Borel and Laplace…